Development and Experimental Validation of a Fluid/Structure-Interaction Finite Element Model of a Vacuum-Driven Cell...

A new fluid/structure-interaction finite element formulation is reported, by means of which reactive fluid stresses can be determined for what is currently the most widely used laboratory apparatus (the Flexercell Strain Unit) for delivering controlled in vitro mechanical stimuli to cultured cells. The apparatus functions by means of cyclic vacuum application to the undersurface of a membrane-like circular rubber substrate. When operated in its original embodiment (i.e., without axial constraint to substrate motion), the pulsatile vacuum causes appreciable pulsatile excursions (often several millimeters) of the substrate. The mechanical stimuli experienced by cells attached atop the substrate include not only substrate distention, but also potentially confounding reactive fluid stresses due to coupled motions of the overlying liquid culture nutrient medium. Since it is impractical to directly measure reactive fluid stress in such environments, a corresponding mathematical model has been developed. The formulation involves transient continuum finite element solutions for the nutrient medium flow field and for the deformation of the substrate, coupled at their mutual interface (the substrate culture surface). Besides the nonlinearities inherent in the flow field and substrate treatments per se, the numerical problem is complicated by the presence of moving boundaries at the nutrient free surface and at the nutrient/substrate interface, as well as by the need to enforce fluid/structure interaction throughout the duty cycle. Algorithmic considerations appropriate to achieving physically realistic numerical performance are reported, and a confirmatory laboratory validation experiment is described.